Estimating Mutation Rates and Sequence Age under a Stochastic Model for Tandem Duplication and Point Mutation

We present a stochastic model for tandem duplications and point mutations that can be used to estimate relative mutation rates and the total number of mutations from a single sequence. Important parameters of the model include the probability of a point mutation and the probability of a tandem duplication of a given length. Our model indicates that if the probability of point mutations is insignificant, little information can be obtained from a single sequence (which has undergone only tandem duplication). In fact, the observed period in a tandem repeat sequence does not necessarily imply that duplications of that length are common. On the other hand, in the presence of both point mutation and tandem duplication, one can estimate the parameters of the model. In particular, the estimate of the total number of mutations can be used to estimate the age of the sequence given that the average number of mutations per generation is known. We validate our model and estimation method via Monte Carlo simulation.